Very interesting legal question. Had it been in a public place, you both would have had right to film anything you pleased. Different deal in the privacy of your home. There, you have the right to record because it's your domicile, even without notice to the officer (e.g. nanny-cams).
However the officer as a private party does not automatically have right to record in somebody else's private space.
I hope that addresses the asymmetry of why one party might be allowed to record and not the other.
There's an error to be made here. Someone might think "If someone else is recording, I can too, since they must have gotten everyone's permission to be recorded". Nuh-uh. They may not have gotten permission because they might not need it. You do, though. Of course, if there's a matter to litigate, you could always take his copy via subpoena.
There's an argument that he might have had a right to record if he obtained the consent of all parties present. But "consent" can't be given unless a person has a bona-fide right to say no: e.g.
- By denying consent (which the officer clearly did not allow),
- By retreating from the space - which makes no sense whatsoever toward the occupants of the home, it's unfair to be forced to leave your own abode simply to maintain your rights; and the officer could stop it anyway by detaining you. Or
- ordinarily an occupant would expel the guest from the home, and that's tricky to manage in the middle of a police search.
As such, I would say it would be impossible for the officer to obtain consent of all parties, since "consent" requires a meaningful ability to say "no".
So now the question is whether he had a right to record as a function of his job. I suspect that is a fast-moving area of "new law", since police body-cams are developing only recently, and as a matter of public policy, they seem to settle a lot of disputes, so I expect them to be strongly encouraged in statute and case law.
But even this raises the question: Did the officer record in a professional capacity or out of a prurient personal interest? Some of that would go to what Department policy is in that case, and that is also informed by whether he used Department-issued equipment.