quantum mechanics - Adding two kets (and Hamiltonians) from two different hilbert spaces?

The combined wavefunction for kets in two different Hilbert spaces

$$|\psi\rangle= c_{11}|11\rangle + c_{1r}|1r\rangle +c_{r1}|r1\rangle +c_{rr}|rr\rangle$$

Where $|ab\rangle = |a\rangle_1 \otimes |b\rangle_2$, and $|a\rangle$ is in a different Hilbert space than $|b\rangle$.

The Hamiltonian for each Hilbert space is say $$H_1 = H_2 = \left( \begin{matrix} A & B \\ C & D \end{matrix} \right)$$

How would you combine $H_1$ and $H_2$ to produce a Hamiltonian that can act on the above $|\psi\rangle$?