“We wanted an open, modern space,” said Mr. Hadzimanovic, who rides a Segway, the self-balancing two wheeler, to the supermarket (and even checks it onto flights).

For the facelift to the first floor, which includes the kitchen, living room, dining area, office and a bathroom, they enlisted their son, who earned an architecture degree from the Swiss Federal Institute of Technology, a university in Zurich known for producing visionaries like the Spanish architect Santiago Calatrava.

The planning involved over two years of family negotiations. The parents wanted to update the exterior to give it a new look; the son didn’t think it was necessary. The son wanted a sunken level; the parents thought it would be too complicated. “Even buying furniture was a democratic process,” said Pe Hadzimanovic, who is writing a book about architecture.

The budget ballooned from an initial $100,000 to $200,000 (including furniture).

Once the design details were complete, out went the gray carpeting, and in came the off-white Italian travertine stone bought in Zurich that “reflects light,” Mr. Hadzimanovic said. Now none of the rooms on the first floor are completely enclosed. The only interior door left is to the first-floor bathroom. In the white-walled entrance foyer, there is now a custom-made, two-sided closet of lacquered fiberboard that holds jackets and purses on the foyer-side, and books and files on the adjacent side, in an office. A rectangular opening 10-inches wide and 20-inches in height, carved into the closet, offers a peek onto the office, which is furnished with a Poul Henningsen PH Snowball lamp and an ochre-colored Eames fiberglass armchair. The cut-out, a motif employed throughout the house, is also aligned to give Mr. Hadzimanovic an unobstructed view down the length of the house onto the back garden while he works. (The cut-out has also turned into a cat door for the Hadzimanovics’ Russian Blue to easily slip into and out of the room.)

Off the foyer is the kitchen, which Pe Hadzimanovic doubled in size, adding more than two dozen teak-paneled drawers and cabinets. He also installed a nearly 12-foot-long glass panel along one wall, one-and-a-half-feet high, to give a view onto the Cypress trees that skirt the side of the house. “I feel linked with nature when I’m in the kitchen,” said Ms. Hadzimanovic, speaking in Serbian. Another cut-out, a 20-by-20-inch square opening, is wedged between a new Electrolux range and Gaggenau wall oven, and also aligned to view the backyard.