Off-hand attacks and damage are also called out under the monk Unarmed Strike ability.
PRD wrote:
Unarmed Strike: At 1st level, a monk gains Improved Unarmed Strike as a bonus feat. A monk's attacks may be with fist, elbows, knees, and feet. This means that a monk may make unarmed strikes with his hands full. There is no such thing as an off-hand attack for a monk striking unarmed. A monk may thus apply his full Strength bonus on damage rolls for all his unarmed strikes.
Given that Pathfinder does not have handedness and you can choose which weapon to start with in a series. The way I would rule it is that which ever weapon you start with is your primary for that round and the other weapon would be your off hand and take the 1/2 STR dmg.