Jessica Simpson's Father Facing Jail Time

TMZ broke the story ... Simpson was popped at a DUI checkpoint in Sherman Oaks, CA earlier this month ... and blew .12 on the breathalyzer test.

Now, we've learned ... the L.A. City Attorney has filed 2 misdemeanor counts of driving under the influence against Papa Joe ... which carry a maximum sentence of 6 months in jail.

If convicted on both counts, Joe could also face up to 36 months probation and a $1,000 fine.