RICHMOND, Va. — Former Gov. Bob McDonnell of Virginia and his wife, Maureen, on trial for conspiring to use his office for personal enrichment, outlined an unexpected defense on Tuesday: Their marriage was so broken that they did not communicate enough to conspire about anything.

In opening arguments in the couple’s corruption trial in federal court here, their lawyers made clear that they planned to rely on the sordid details of their unhappy union as the basis of their legal defense. It was the first time the McDonnells’ version of events had been heard in a widely publicized case that for months has been characterized by the lengthy indictment against them, which charges the couple with accepting more than $165,000 in cash and luxury gifts from a Virginia businessman.

Ms. McDonnell, her lawyer said, had a “crush” on the businessman, Jonnie R. Williams Sr., the prosecutors’ star witness, who the government said would detail the designer clothing, vacations, golf rounds and cash he provided in exchange for the governor’s help in promoting his company, which made a dietary supplement.

Mr. Williams was a frequent visitor to the Executive Mansion, where he and Ms. McDonnell would meet privately. He was known as “Maureen’s favorite playmate,” the lawyer, William A. Burck, told jurors. “Maureen McDonnell and Jonnie Williams had a relationship some would consider improper for two people not married.”