Generally we write them the same way that we do for homonuclear diatomics (1-sigma, 1-pi, 1-pi*, etc). The composition of those molecular orbitals in terms of constituent atomic orbitals can be a little more difficult to figure out due to the different energies of those constituent atomic orbitals (i.e., the energy of the 2s orbital on carbon is different from the 2s atomic orbital energy on oxygen).
Do note that interactions between atomic orbitals depend on energy gap, overlap, and symmetry, so in principle the atomic interactions in heteronuclear and homonuclear molecules are exactly the same in character. It is the strength of those interactions that changes as the energies of the atomic orbitals begin to diverge. Consider for example a homonuclear diatomic A-A. The lowest lying sigma bond will primarily be formed, maybe, as an interaction between the 2s (valence) orbitals of the two As. But that's a simplified picture. The 1s orbitals also contribute because they have the appropriate symmetries. But, the strength of the contribution also depends on the energetic matching; the 1s orbitals have such different energies than the 2s orbitals, and their overlap is not as great (because they are smaller), so their contribution is really almost negligible. So, we usually just approximate the bond as being only between the 2s orbitals. In a heteronuclear diatomic, A-B, it is the same situations, but all the relative energies are different, so in some cases the contribution of non-like atomic orbitals may not longer be neglected.
The thing to keep in mind is that molecular orbitals are not just mixtures between two atomic atomic orbitals. You take ALL the molecular orbitals on one nucleus and mix them with ALL the molecular orbitals of the other nuclei. It just so happens that often times the molecular orbitals that fall out are PRIMARILY the result of mixing only between two atomic orbitals - and that's the way we often draw MO diagrams for educational purposes. But in, say, computational calculations, those minor interactions are included because they can make a small but not-negligible difference in calculating accurate structures and properties. Those minor interactions become more important (larger in magnitude) when the nuclei are not the same, so it can become more difficult to draw simple MO diagrams and determine what the major inter-atomic interactions are.