```python
import numpy as np
from pyscf import gto, scf, dft, ao2mo
from pyscf.lib import logger

def compute_coupling_matrix(mol1, mol2, basis='cc-pVDZ', method='CIS'):
    # Define molecules
    mol1 = gto.M(atom=mol1, basis=basis)
    mol2 = gto.M(atom=mol2, basis=basis)

    # Perform DFT calculation to get molecular orbitals
    mf1 = dft.RKS(mol1)
    mf1.xc = 'B3LYP'
    mf1.kernel()

    mf2 = dft.RKS(mol2)
    mf2.xc = 'B3LYP'
    mf2.kernel()

    # Perform CIS calculation for excited states
    from pyscf import ci
    cis1 = ci.CIS(mf1)
    e1, c1 = cis1.kernel()

    cis2 = ci.CIS(mf2)
    e2, c2 = cis2.kernel()

    # Compute intermolecular 2e integrals in AO basis
    mol12 = gto.mole.conc_mol(mol1, mol2)
    ao2e = ao2mo.kernel(mol12, mol12.ao_labels())

    # Transform 2e integrals to MO basis
    mo_coeff = np.hstack((mf1.mo_coeff, mf2.mo_coeff))
    mo2e = ao2mo.incore.general(ao2e, (mo_coeff,)*4, compact=False)

    # Compute J and K couplings
    J_coupling = np.einsum('pqrs,pr->qs', mo2e, np.dot(c1.T, c2))
    K_coupling = np.einsum('psrq,pr->qs', mo2e, np.dot(c1.T, c2))

    # Compute DFT XC contributions
    # This is a simplified approach, in practice, you might need to compute these integrals explicitly
    # or use existing DFT functional derivatives.
    xc_contrib = mf1.get_veff() - mf2.get_veff()

    # Evaluate overall coupling term
    coupling_matrix = J_coupling - K_coupling + xc_contrib

    return coupling_matrix

# Example usage
mol1 = 'H 0 0 0; F 0 0 1.1'
mol2 = 'H 0 0 2.2; F 0 0 3.3'
coupling_matrix = compute_coupling_matrix(mol1, mol2)
print(coupling_matrix)
```