This is rule #3 from Canopy Financial's 2009 "HSA Road Rules". Hopefully it is still a reliable source.
"You cannot be covered by any other health insurance that reimburses you for health expenses you incur, unless it is another HSA-qualified HDHP. If a family has all its members covered under two HSA-qualified HDHPs, or some family members are on one qualified plan and the other family members are under another qualified plan, the maximum annual contribution to the account remains in force. Just because you have coverage with two HSA-qualified HDHPs does not mean you can double your HSA contribution. "
Don't forget about any catch ups :)