Here is the list of Washington State Highways Closed to Bicycles:
WSDOT - Washington State Highways Closed to Bicycles

And on the state bicycle map of Washington, it will indicate where a highway is closed to bicycles. It does that as well on the Oregon bicycle map, but they go the extra step of listing out the specifics of the "bicycles prohibited" on the back of the map. For example, I can ride the entirety of I-84 to the Idaho state line from milepost 10.25 eastbound (NE 122nd Ave), or milepost 15.14 westbound (Sandy Blvd).

As far as I know, it is legal to ride the interstates/freeways on many of the states west of the Mississippi, except where it's prohibited. The prohibitions are usually in urban areas or where the shoulder is going to be compromised. And this is regardless of whether there is another road paralleling the freeway, or a better option for bicycles exist.