Your DMM may be high resistance, but it has an intrinsic capacitance, and when you touch the probes to your circuit, the capacitance undergoes a charge transfer either from or to your circuit.Try putting a 100K ohm resistor in series with each lead of your DMM probe.I've fought this same problem with a high end Fluke DMM in a ATE usage, every time the relay closed, the circuit (in my case it was a comparator with hysteresis) flipped states.