Combine two mesh filters into one

I am procedurally creating two meshes, and then trying to combine them into one mesh, add that mesh to an object’s mesh filter.
My procedurally created mesh works correctly. I add it as a mesh filter to an object and you can visually see it (190 verts, 324 tris).

When I create another mesh (the same one, for example) it is not visible. When looking in the inspector, you can see that it is apart of the mesh filter, and there is a mesh renderer component. When looking at the mesh itself, you can see it has the expected double amount of verts and tris (380, 648). It’s there, but not there…

Here is the combineMesh code I use

public static Mesh CombineMeshes(string name, Mesh mesh0, Mesh mesh1)
{
    CombineInstance[] combine = new CombineInstance[2];

    combine[0].mesh = mesh0;
    combine[1].mesh = mesh1;

    Mesh mesh = new Mesh();
    mesh.CombineMeshes(combine);
    mesh.name = name;

    return mesh;
}

Maybe the meshes are sharing the same locations in space?