Sounds to me like your headlight fuse, which is a little "metal box" in your fuse panel and acts like a circuit breaker, is shutting off your lights when you put on the highbeams. It took a minute before your lights came back on, right? That's when it kicks back on, after cooling off.
Like everyone is saying, something is shorting out, causing the "shut-off" to kick in. Is it just possible you need a higher amp headlight fuse in your panel? Or, it may also be possible that your headlight fuse itself is faulty ... aside from the above solutions, this may be something else to consider.
