It is a requirement that all students at the University of California meet the university’s own health insurance mandate. Luckily, as soon as you are registered with your course you will automatically be enrolled in the Berkeley Student Health Insurance Plan (SHIP). In doing so, you meet this mandate. SHPI covers medical, counselling, prescription, vision and dental services.
Most large companies are required to offer all full-time employees health insurance for the entire length of their contract. However, interns are sometimes classed as seasonal or variable-hour employees, and so the company may not be obliged to offer anything. For unpaid interns, companies are not obliged to offer health insurance, and you’ll need to sort out your own private plan.
Do your research into private health insurance as plans are expensive. However, they are substantially less expensive than the bill you’ll receive if you require any medical treatment out there. As a ballpark figure, expect to pay several thousand euros to cover your stay, though realistically it’s impossible to put an "average" value on health insurance in the States since US health care is pretty volatile.