Professor Thurman, a former monk himself, describes himself as a friend and admirer of Mr. Roach, and said that after the geshe made his relationship with Ms. McNally public in 2003, he begged him to renounce his monastic vows and to stop wearing the robes that mark him as a member of a monastic order. Mr. Roach declined, and the two have not spoken since.

“He is doing this partnership thing and insisting on being a monk,” Professor Thurman said. “It is superhuman. He says he is staying celibate, but people find it hard to believe.”

The yurt in which Mr. Roach and Ms. McNally live when they are not traveling the world (which is often about half the year) sits in the high desert some 100 miles east of Tucson, on a platform overlooking a rift in the cactus-speckled hills. For 100 acres around, the land is the property of Diamond Mountain University, an unaccredited school that Mr. Roach founded with Ms. McNally in 2004 to teach Buddhist principles and translation skills.

Although devoid of modern conveniences, the yurt they live in, which is 22 feet in diameter, feels almost luxurious compared with the spare, desiccated landscape around it. On one side of the tent is their double bed, and beside it a commode elegantly disguised as a wood side table. The floor is covered with carpets. A few carved wooden chests hold clothes and pillows.

Light streams in from a hole at the center of the tent’s roof, illuminating its poles, which were imported from Mongolia. The closeness to nature means that the indoor temperature is essentially the ambient one — beyond baking in the summer and freezing in the winter. (Their one attempt to battle the elements is a wood-burning stove.)

The couple did a three-year silent retreat in this yurt from 2000 to 2003, while their relationship was a secret to all but the few people who brought them food. Soon afterward, Mr. Roach determined it should be public, even if it flew in the face of two millenniums of Tibetan Buddhist tradition.

He acted for two reasons, he said. One, he felt that it was impossible to keep secrets in this age of Google Earth. Two, he decided that if Buddhism was really going to succeed in America, it would have to be more inclusive of women.