I mailed this to the whatwg list, but getting a bug on file seems better:

It would be very useful to be able to send structured data, including
Blobs, through the BroadcastChannel API.

This is something we've seen any time we've done storage or message
passing, that one of the first thing authors ask for is to not have to
do JSON serialization/parsing manually. The ability to pass
ArrayBuffers and Blobs is somewhat less commonly asked for, likely
because binary data is less often used, but seems important
nonetheless.

We can't allow transferring of objects, since you can't transfer
something to all listeners of a broadcasting API. But plain structured
clones should be no problem to support conceptually (though more work
to implement of course).

We've started looking at doing structured clone support for Firefox
and likely won't ship until we have that implemented.