By Janice Hardy, @Janice_Hardy
Q: Can you mix first and third POVs?
Short answer: Sure.
Long answer: Like everything else in writing, it's all in how you do it. Kathleen Duey's Skin Hunger mixed first and third with great success, as does Roland Smith's I.Q. series. But I've read books that didn't mix them so well and made an utter mess of the story. Every POV switch was painful, there was no reason for them, and it just yanked me right out of the tale.
Mixing POV styles can be jarring to the reader without a good reason to do it. In Skin Hunger, the POVs are set 500 years apart, and the present day POV is in first person, while the past is in third. The more detached third person works well thematically with the distant story of the past. In the I.Q. series, the third person POV is snippets of the bad guys, so seeing them from a more distant perspective also worked thematically.
First and third mixed in the same time frame with two major POV characters doesn't always work so well, however, because there's often no reason for it to occur. It's done just to be different, or because you want to be able to show something your protag can't know and this is an easy way to do it.
If the reasons behind the POV mix are sound and serve the storytelling, go for it. If not, I'd suggest picking one and sticking with it. Mixing them is tough to do well, so unless it's the best thing for the story, you might be better off with one style.