He must have had the interview yesterday.
(Él) debió haber tenido la entrevista ayer.

(Él) debía haber tenido la entrevista ayer.
He should have had the interview yesterday.
He would have had the interview yesterday.
(Él) hubiera tendido la entrevista ayer.

(This can be "should have" or "would have", it depends on the context of the sentence.)
He was supposed to have the interview yesterday.
(Él) debería haber tenido la entrevista ayer.
He must have had the interview already.
(Él) debió haber tenido ya la entrevista.

(Él) debía haber tenido ya la entrevista.
Hope that helps