Unless there is good reason to believe that the Tsarnaev brothers were acting as agents of al Qaeda or some other AUMF-covered group, talk of putting Dzhokar Tsarnaev into military custody as an enemy combatant makes no legal sense, for the reasons that Ben Wittes explains in this excellent post from Jacob Gershman at the Wall Street Journal's Law Blog. But in any event, it is a bad and unnecessary idea when it comes to a person captured within the United States itself.
The issue at hand now that Tsarnaev has been captured is interrogation, to be sure. But it does not follow that the best immediate disposition option is thus military custody (and it is perfectly clear that the best long-term disposition option in this instance is prosecution).
Yes, FBI custody normally would be followed by Miranda warnings, and more to the point the FBI in run of the mill circumstances would not persist in questioning a person if they invoke their right to silence and would not do so without counsel present if they invoke their right to counsel. But that doesn't mean the FBI can't chart a different course when public safety is an exigent concern, nor that other government officials--including the interrogation specialists from the High-Value Interrogation Group, or HIG--cannot become involved. If this unconventional path is taken, the risk the government runs is that the fruits of the interrogation will prove inadmissible at trial. To be blunt, that's probably not a big deal in this case, given the mass of evidence from other sources that will be available as to Tsarnaev himself...though if Tsarnaev implicates third persons, the prospect of inadmissibility becomes more significant. Then again, it is not even obvious that this risk would be realized, given the Quarles public-safety exception. Don't forget DOJ's promise to exploit this to the hilt in terrorism cases, as Ben explained here two years ago.
The point of Quarles is that the government might still get to use the fruits of an un-Mirandized interrogation in a subsequent court proceeding, if the interrogation was for purposes of assuring public safety rather than obtaining evidence. No one can say with confidence how long a time-window is available under Quarles. A fact pattern like this one no doubt will tempt the courts to be fairly flexible, though whether that means a window of hours or even days is anyone's guess. At any rate, the bottom line is that it is not necessary to abandon the criminal justice system in order to conduct an un-Mirandized interrogation of Tsarnaev. He is in custody; he will be easily convicted and presumably face capital punishment; and he can and will be interrogated appropriately in the meantime. There is not a strong case for a military solution here.