But you don't need to put the military under the direct command of the civilian president like US does, if parliament can take military action against the civilian president and civilian action against the military leader then they have ways to deal with both.

American president is too powerful to deal with since he controls both the civilian and the military side.

This is the one argument left for monarchy; that the military in the UK (and technically Australia) swear loyatly to the monarch, not the Prime Minister. In the event of an obviously-lunatic elected official ordering the troops into civilian areas to "pacify" civilian populations, the monarch could (in theory) countermand that order.

There's a mechanism by which Congress can remove the president if he gets out of control.