[@Sagittarius] Oh, right...

The majority of Beorcs dislike Laguz under a combination of a racial superiority complex and a false belief that the Laguz were giving in to the dragons by trying to harness their power. Beorc-Laguz hybrids are existent, just as some Beorc-Laguz settlements and relations are, but all are rare and kept secretive from both races.
Such hybrids are known as Branded; they look mostly like Beorc, except for a certain birthmark on their body unique to them. They cannot shift forms like Laguz can, but may bear certain Laguz traits that Beorc do not, such as heightened senses, abnormally high aptitude, or some special technique (reflected in one of your features). Branded function as Beorc in gaining stats and proficiency (via promotion), but gain class features like a Laguz (per the end of each Act, independent of their class).

As of right now, no half-Manaketes could possibly exist, in terms of the active story, and if any were made in the course of the story, they certainly would not become mature enough to matter. If you must know, however, such hybrids are ultimately akin to Branded (in that they gain a certain mark on their body and some advanced trait), but they will live being even [i]more[/i] racially prejudiced.
If that sounds underwhelming, remember: the Manaketes are dragons brought down to the power level of humans. Their blood wouldn't have any particularly special power to pass down. And no, it wouldn't make them resonant to a Dragonstone, either.