The Gemara cites a machlokes between Rav and Shmuel as to what the reward of "batim" mean with respect to the midwives. One says it means bais malchus and the other says batei kehunah and leviya.
1. According to the opinion of batei kehuna/ leviya how is that a reward for Miriam? The kohanim and Leviyim did not come from her.
A thought that I had as a possible answer is that this opinion was given according to the opinion that holds that shifra and puah were yocheved and elisheva and as Aarons wife her sons were kohanim.
Your answer is indeed the answer of the Maharsha (who also states that the answer of Beis Malchus must hold it was Yocheved and Miriam). The Maharsha explains that "Batei Leviyah" refers to the fact that Yocheved merited that Amram (who was a Levi) should remarry her and have Moshe Rabeinu, the father of all Levi'im.
All the best,
However, according to the opinion that said bais malchus- 1. Was malchus the reward for Miriam and Yocheved? And 2. Why does the pasuk say batim if it only is referring to bais malchus. It should have said bayis.
Also, it is interesting to note that Rashi on the pasuk in shemos combines the two opinions and says that batim refers to batei kehuna, batei leviya and batei malchus. He does not bring down the machlokes.
Any thoughts on that.
1. Yes, as the Malchus came from both of them.
2. It is possible that Batei Malchus is appropriate as the king's family and associates throughout Nevi'im are always known as "Beis David," (l'Havdil) "Beis Yeravam," "Beis Achav," etc. Batei Malchus therefore refers to the various "Batim" of the various kings of Klal Yisrael.
Regarding Rashi, Rashi often applies (instead of just quoting) the Gemara to explain the Pasuk, often coming up with a "new opinion." Being that Rashi earlier said that the Pasuk is referring to Yocheved and Miriam, and it is undisupted that Kehunah, Leviyah, and Malchus came from Yocheved and Miriam respectively, it makes sense to say that they received these rewards because of their good deeds.
All the best,