diff --git a/.github/workflows/test_on_push.yml b/.github/workflows/test_on_push.yml
index 5701b555e0..f256607e2d 100644
--- a/.github/workflows/test_on_push.yml
+++ b/.github/workflows/test_on_push.yml
@@ -30,7 +30,7 @@ jobs:
           python -m pip install pre-commit
           pre-commit run -a
 
-  run_unit_tests:
+  run_unit_integration_and_coverage_tests:
     needs: style
     runs-on: ${{ matrix.os }}
     strategy:
@@ -38,11 +38,7 @@ jobs:
       matrix:
         os: [ubuntu-latest, macos-12, macos-14, windows-latest]
         python-version: ["3.9", "3.10", "3.11", "3.12"]
-        # We check coverage on Ubuntu with Python 3.12, so we skip unit tests for it here
-        exclude:
-          - os: ubuntu-latest
-            python-version: "3.12"
-    name: Unit tests (${{ matrix.os }} / Python ${{ matrix.python-version }})
+    name: Tests (${{ matrix.os }} / Python ${{ matrix.python-version }})
 
     steps:
       - name: Check out PyBaMM repository
@@ -109,144 +105,24 @@ jobs:
         if: matrix.os != 'windows-latest'
         run: python -m nox -s pybamm-requires
 
-      - name: Run unit tests for ${{ matrix.os }} with Python ${{ matrix.python-version }}
-        run: python -m nox -s unit
-
-  check_coverage:
-    needs: style
-    runs-on: ubuntu-latest
-    strategy:
-      fail-fast: false
-    name: Coverage tests (ubuntu-latest / Python 3.12)
-
-    steps:
-      - name: Check out PyBaMM repository
-        uses: actions/checkout@v4
-
-      - name: Install Linux system dependencies
-        uses: awalsh128/cache-apt-pkgs-action@v1.4.2
-        with:
-          packages: gfortran gcc graphviz pandoc
-          execute_install_scripts: true
-
-      # dot -c is for registering graphviz fonts and plugins
-      - name: Install OpenBLAS and TeXLive for Linux
+      - name: Run unit/coverage tests for ${{ matrix.os }} with Python ${{ matrix.python-version }}
+        shell: bash
         run: |
-          sudo apt-get update
-          sudo dot -c
-          sudo apt-get install libopenblas-dev texlive-latex-extra dvipng
-
-      - name: Set up Python 3.12
-        id: setup-python
-        uses: actions/setup-python@v5
-        with:
-          python-version: 3.12
-          cache: 'pip'
-
-      - name: Install nox
-        run: python -m pip install nox
+          if [ ${{ matrix.python-version }} == "3.12" && ${{ matrix.os }} == "ubuntu-latest" ]; then
+            python -m nox -s coverage
+          else
+            python -m nox -s unit
+          fi
 
-      - name: Cache pybamm-requires nox environment for GNU/Linux
-        uses: actions/cache@v4
-        with:
-          path: |
-            # Repository files
-            ${{ github.workspace }}/pybind11/
-            ${{ github.workspace }}/install_KLU_Sundials/
-            # Headers and dynamic library files for SuiteSparse and SUNDIALS
-            ${{ env.HOME }}/.local/lib/
-            ${{ env.HOME }}/.local/include/
-          key: nox-${{ matrix.os }}-pybamm-requires-${{ steps.setup-python.outputs.python-version }}-${{ hashFiles('**/install_KLU_Sundials.py', '**/noxfile.py', '**/test_on_push.yml') }}
-
-      - name: Install SuiteSparse and SUNDIALS on GNU/Linux
-        timeout-minutes: 10
-        run: python -m nox -s pybamm-requires
-
-      - name: Run unit tests for Ubuntu with Python 3.11 and generate coverage report
-        run: python -m nox -s coverage
+      - name: Run integration tests for ${{ matrix.os }} with Python ${{ matrix.python-version }}
+        run: python -m nox -s integration
 
       - name: Upload coverage report
+        if: matrix.os == 'ubuntu-latest' && matrix.python-version == '3.12'
         uses: codecov/codecov-action@v4.4.1
         with:
           token: ${{ secrets.CODECOV_TOKEN }}
 
-  run_integration_tests:
-    needs: style
-    runs-on: ${{ matrix.os }}
-    strategy:
-      fail-fast: false
-      matrix:
-        os: [ubuntu-latest, macos-12, macos-14, windows-latest]
-        python-version: ["3.9", "3.10", "3.11", "3.12"]
-    name: Integration tests (${{ matrix.os }} / Python ${{ matrix.python-version }})
-    steps:
-      - name: Check out PyBaMM repository
-        uses: actions/checkout@v4
-
-      - name: Install Linux system dependencies
-        uses: awalsh128/cache-apt-pkgs-action@v1.4.2
-        if: matrix.os == 'ubuntu-latest'
-        with:
-          packages: gfortran gcc graphviz pandoc
-          execute_install_scripts: true
-
-      # dot -c is for registering graphviz fonts and plugins
-      - name: Install OpenBLAS and TeXLive for Linux
-        if: matrix.os == 'ubuntu-latest'
-        run: |
-          sudo apt-get update
-          sudo dot -c
-          sudo apt-get install libopenblas-dev texlive-latex-extra dvipng
-
-      - name: Install macOS system dependencies
-        if: matrix.os == 'macos-12' || matrix.os == 'macos-14'
-        env:
-          HOMEBREW_NO_INSTALL_CLEANUP: 1
-          HOMEBREW_NO_AUTO_UPDATE: 1
-          HOMEBREW_NO_COLOR: 1
-          # Speed up CI
-          NONINTERACTIVE: 1
-        # sometimes gfortran cannot be found, so reinstall gcc just to be sure
-        run: |
-          brew analytics off
-          brew install graphviz libomp
-          brew reinstall gcc
-
-      - name: Install Windows system dependencies
-        if: matrix.os == 'windows-latest'
-        run: choco install graphviz --version=8.0.5
-
-      - name: Set up Python ${{ matrix.python-version }}
-        id: setup-python
-        uses: actions/setup-python@v5
-        with:
-          python-version: ${{ matrix.python-version }}
-          cache: 'pip'
-
-      - name: Install nox
-        run: python -m pip install nox
-
-      - name: Cache pybamm-requires nox environment for GNU/Linux and macOS
-        uses: actions/cache@v4
-        if: matrix.os != 'windows-latest'
-        with:
-          path: |
-            # Repository files
-            ${{ github.workspace }}/pybind11/
-            ${{ github.workspace }}/install_KLU_Sundials/
-            # Headers and dynamic library files for SuiteSparse and SUNDIALS
-            ${{ env.HOME }}/.local/lib/
-            ${{ env.HOME }}/.local/include/
-          key: nox-${{ matrix.os }}-pybamm-requires-${{ steps.setup-python.outputs.python-version }}-${{ hashFiles('**/install_KLU_Sundials.py', '**/noxfile.py', '**/test_on_push.yml') }}
-
-      - name: Install SuiteSparse and SUNDIALS on GNU/Linux and macOS
-        timeout-minutes: 10
-        if: matrix.os != 'windows-latest'
-        run: python -m nox -s pybamm-requires
-
-      - name: Run integration tests for ${{ matrix.os }} with Python ${{ matrix.python-version }}
-        run: python -m nox -s integration
-
   # Skips IDAKLU module compilation for speedups, which is already tested in other jobs.
   run_doctests:
     needs: style