Question: Does the punishment of the grave include the disobedient mu’min or is it specific for the kaafir?
Answer: The ceaseless punishment of the grave is for the munaafiq (hypocrite) and for the kaafir (disbeliever).
As for the disobedient mu’min (believer) then he may be punished in the grave because it is established in the Saheehain (the two Saheehs) from the hadeeth of Ibn ‘Abbaas (رضى الله عنهما) that the Prophet (صلى الله عليه وسلم) while passing by two graves said: “They (their occupants) are being tormented, but they are not tormented for a grievous sin. One of them did not keep himself safe from being defiled by urine and the other carried tales (nameemah).” 
And it is well known that they (the occupants of the graves) were Muslims.
 Reported in Saheeh Bukhaari and Muslim. Narrated Ibn ‘Abbaas: The Prophet once passed by two graves and said, “These two persons are being tortured not for a major sin (to avoid). One of them never saved himself from being soiled with his urine, while the other used to go about with calumnies (to make enmity between friends).” The Prophet then took a green leaf of a date-palm tree, split it into (pieces) and fixed one on each grave. They said, “O Allaah’s Apostle! Why have you done so?” He replied, “I hope that their punishment might be lessened till these (the pieces of the leaf) become dry.”