Once the police arrest anyone, the police can ask questions. The individual under arrest has the right not to answer and the right to have an attorney present during the questioning i.e., "miranda rights"
"The person in custody must, prior to interrogation, be clearly informed that he or she has the right to remain silent, and that anything the person says will be used against that person in court; the person must be clearly informed that he or she has the right to consult with an attorney and to have that attorney present during questioning, and that, if he or she is indigent, an attorney will be provided at no cost to represent her or him."
The standard to arrest someone is pretty low. People are arrested and interrogated every day with far less to implicate than what the police appear to have against this husband. I'm wondering why they have yet to arrest their sole person of interest--in a missing person case, where time is against the police. Like I said, arrest him, book him, take prints and all the rest of the process, sit him in an interrogation room and make it all very real for him. Sure, his lawyer will be there and most likely he doesn't answer any questions. But that doesn't mean they can't make him sit there and listen to their questions and watch his demeanor etc. Who knows, maybe the husband gets cocky and decides to respond to some of their questions. Or maybe the realness of being arrested and questioned in a police station causes him to break down and spill everything.