Microphones disturbed by capacitance
I've used multi-channel NI analogue acquisition cards and they have a single ADC which can be programmed to connect to one of the mulitple-inputs by a multiplexer chip. Channels not un-connected to the ADC will float high and, when that channel "connects" it will glitch. 

You need a pull-down resistor on the inputs so that if there is leakage current from the mulitplexer, it has a path to ground. Probably something in the order of 3k3. It's easy to try and hopefully this advise works.