Half slave and half free to the Rambam eats neither from his own Passover nor from his master. To the Raavad he eats from his own..The issue is which way is like the later mishna. The Raavad holds  his own is like the later mishna. The Rambam is holding it was the first mishna that held he eats of his own. The later Mishna said he must be let to go free since he can not be married to a Israelit [female Israeli], nor can he be married to a slave woman because he is half free.

Tosphot in Bava Batra asks on this that letting him go free is transgressing a lav/negative prohibition. And he answers that being married to a Israelit is a positive command which pushes off a negative command.  

[Half slave half free means owned by two masters, but one freed him. So he is now half free. The point of freeing him completely is that as a slave he can have a slave wife. As free he can have a regular Israelit. But half and half he can have neither, so he must be freed.]

Rav Shach pointed out a reason the Rambam took the approach that he did. I.e that the first mishna held women do not need to be appointed on any specific passover. [This opinion is brought in the Rosh in Nedarim page 36 side A] [And thus neither do slaves.]  So it makes sense that a 1/2 slave 1/2 free person would be able to eat from his or her own passover and not be required to join the with the group of his master. [But then why he eats only his own? Why could he not also eat from his masters passover?] But the later mishna holds that women do need to be appointed on a specific passover, so a half slave and half free person would thus not be able to eat of neither his own nor that of his master unless he is totally set free.