Ignoring that these two are both males - - the two species probably never (or only very rarely) mate with one another in nature; however, in the laboratory they can be cross bred. As I recall they will produce fertilized eggs, but most never hatch, and none survive to adulthood (but I'd need to look it up to refresh my memory). So. the two species are genetically different enough that hybrids between them are very unlikely to ever occur. However, they are both in the subgenus Pterourus, and they are fairly closely related (as compared to other species you might see such as the Black Swallowtail or Giant Swallowtial, which are much less related). If you look at the pictures of the caterpillars, you'll see that they are fairly similar.

Boy if you could get a hybrid from them, I'll bet it would be one spectacular butterfly!

A beautiful shot of two very closely related (though very different looking) species.

Moved from ID Request.

On the left, Eastern Tiger Swallowtail.
On the right, male Spicebush Swallowtail.
Nice shots!

I believe both your butterflies are Eastern Tiger Swallowtails. The Eastern Tigers have a dark morph that mimics the Spicebush Swallowtails, and is common in Southeastern U.S.