08/15/2012 at 03:00 PM EDT
Joe Simpson was charged on Tuesday with two misdemeanor counts of driving under the influence.
The 54-year-old father of Jessica Simpson
and Ashlee Simpson
was arrested on Aug. 4
after he was pulled over at approximately 10 p.m. on Ventura Boulevard in the Sherman Oaks area of Los Angeles.
"He had had a couple of glasses of wine at dinner with his wife. They were driving home and he went through a check point a few blocks from the restaurant," a source close to Joe Simpson tells PEOPLE.
"He took a breathalyzer voluntarily thinking nothing of it. He was surprised to know that he was over the limit. He learned a very important lesson from it all."
If convicted, he could serve up to six months jail time, pay a $1,000 fine and face 36 months of probation, the Los Angeles City Attorney's office tells PEOPLE.
Simpson, who spent the night in jail following his arrest, was reportedly released at 9:41 a.m. the next morning.
His arraignment is scheduled for Aug. 30 in L.A.