The Girls' Day School Trust, which runs 29 schools in England and Wales, wants the requirement to work in different types of schools written into all teachers' contracts.
Barbara Harrison, chief executive, said working across the sectors should be part of teachers' continual training through their careers.
"At the moment there is no need for a teacher to step outside the comfort zone that they work in," she said. "Changing that would certainly create more rounded teachers. Having teachers work in both types of school would create understanding and break down barriers. It could be very powerful."
Secondary school teachers should also spend time working in primaries and vice versa, Ms Harrison said. The move would allow teachers to develop a better understanding of how children develop at different stages of their education.
Ms Harrison made the suggestion yesterday, at a seminar hosted by the trust and Civitas, the right-wing think-tank.
Andrew Adonis, the junior minister for schools, also addressed the conference about ending the independent and state school divide.
Under the trust's proposal, teachers would work on a placement in other types of schools. This could be concentrated in a block or spread out over a year.
The trust is planning to launch a pilot scheme of staff exchanges with about 50 teachers from its schools. It already runs smaller-scale projects in its schools, including masterclasses in primaries.
Wimbledon High, a trust school in south-west London, and King's College School for boys in Wimbledon, work with five state schools as part of London Challenge. Teachers run masterclasses and Easter revision sessions for pupils.
Pamela Wilkes, head of Wimbledon High, said: "We gain as much and sometimes more than the maintained sector. The teaching is often fantastic because they have to work harder to motivate their students."
Belvedere, a trust school in Liverpool, became one of the first two independent schools to switch to the state sector by becoming an academy in September last year. Another trust school, Birkenhead High, on Merseyside, will become an academy next year.
David Green, director of Civitas, told the seminar that removing the barriers to opening new schools was the best way to improve standards in deprived areas. Richer parents already monopolised the best state schools, leaving poorer families with low-performing schools.
Dr Green advocated a voucher system, similar to one used in Sweden, where parents could pay for a place at any school, including independent schools, which are banned from charging top-up fees.
Profit-making companies should be free to open and run state schools where there is parental demand for higher standards, he said.