B737 First Officer reports a dual DC Fail caution light during climb at FL310. The Captain inadvertently reads from the IRS fail checklist and places both IRS switches to the ATT position freezing both attitude displays. An emergency was declared and flight diverted to nearest suitable airport.

Narrative

During climb through about FL310; we experienced a dual DC Fail on the IRS's. I was executing a modified max angle climb due to moderate turbulence reported in front of us. We could see the clouds that we thought were causing it so we were trying to get to cruise prior to reaching the line of clouds. The radio was very congested. The pilot not flying directed me to continue flying up to FL340; which was our clearance limit. The pilot not flying started the DC Fail Checklist; read through it once; and then proceeded to read the notes on the left page of the checklist. We checked the battery and it read 0 volts. We discussed a plan and then; without really informing me; the pilot not flying went back into the checklist and proceeded to read from the IRS Fault/Failure Checklist. He then turned the IRS switches to ATT. This kicked off the autopilot and froze the HSI's. Right at that moment; I was IMC in the climb. I told the pilot not flying that I just had a failure of the IRS's and then I looked up and saw that they were in ATT. I then knew what had happened. I told the pilot not flying that we needed to exit RVSM airspace and that I wanted a quick descent to VMC since I knew it was clear below and in front of us. The pilot not flying concurred and since I had the radios; I coordinated a descent with ATC. I ballooned to just above FL340; the Controller gave me the descent; and I proceeded to descend. We broke out of the cirrus clouds at that time and we proceeded visually to ZZZ and landed. We did declare an emergency and I don't believe I exceeded any altitude tolerances; but there was a lot going on right at that time.