Dave, as Mike says, this is a lot easier with a SLR and Wide Angle lens. And a dome port, the bigger the better.
There's two big issues: Focus and Exposure.
The focus issue is that underwater, the dome port creates a "virtual image" that the lens focuses on; this varies from 18" to 6" depending on the size of the dome. Out of the water, though, the dome port has no influence on focus.
So, when shooting an over-under, you will need a depth of field from infinity to your virtual image. This is a piece of cake for a (film)16mm (DSLR)10.5mm fisheye, and not that tough for a (film)20mm (DSLR)14mm rectilinear wide angle. Be aware that you'll need about f22, so you may have a slowish shutter speed.
If you have to use a diopter for your dome port in "normal" underwater shooting, then you may have to use a special split diopter. This diopter has been cut in half, so the above water half has nothing in it. These are tough to find off the shelf unless you use Cokin filters, and then only the "A" filters have a chance of fitting into a dome. Subal also makes some, which can be special ordered from a dealer (bring your checkbook!).
So, with the focus issue taken care of, then there's the exposure issue. Depending on the water conditions, you may have 2 to 3 stops of difference between the "air side" exposure and the "water side". Stack on another filter, one with split Neutral Density/clear. I have gotten away without this when shooting in very shallow water over white sand, though, so a bit of planning will help. These filters are fairly easy to find.
A last point is that the center of curvature, for the dome, needs to be exactly at water level; otherwise you end up with a sliver of sky and the horizon obscured (too low) or a view of the top of the water and your fins (too high). As Mike says, try it first in a pool...you'll be glad you did.
There's a few other trivial items, like reflections in the dome, water droplets, and motion blur at the interface, but you'll work those out with practice.
All the best, James