The California Zephyr is the best-known example of mix and match passenger trains, but there were others. Beginning in the mid-1950's, the UP and the Milwaukee Road jointly operated the "City" trains between Chicago and Omaha. The train would run behind Milwaukee Road power and there would be some Milwaukee Road cars to provide Chicago-Omaha service. Between Omaha and the western destinations, the trains were all UP. This arrangement is why the Milwaukee repainted its passenger cars in UP yellow. Before 1955 or so, the UP had a similar arrangement with the C&NW.
Railroads also might lease locomotives or cars from other roads to overcome a temporary shortage of capacity. I've seen a published photo of a couple of PRR passenger cars in a Milwaukee Road train, although I'm not sure that is why they were there. The Milwaukee leased a bunch of diesels from the Southern Railway in the 60's or 70's and I've seen some photos of mixed consists of Milwaukee and Southern diesels.
Freight trains, of course, were almost always mixed. A steam era train hauling general freight was typically 40-60% home road cars, but more or less than that would not be especially unusual or un-prototypical. The longer the run, the greater the variety of cars. Coal trains, on the other hand, would typically be all home road cars.
Passenger steam engines were not often used to pull freight, simply because they didn't have the tractive effort to start a heavy train. The exception was that sometimes the railroad would use a fast Pacific or Hudson to pull a fast reefer block. I've even seen one photo of a 4-6-4 Hiawatha streamliner pulling a train of reefers. This was in the waning days of steam when the big steamers had mostly been displaced by diesels in passenger service, and the railroad was trying to get the last bit of revenue out of the steamers before scrapping them.
Then, of course, there is always the branch line "mixed train" with one coach or combine hung on the end of a short local freight. Or you can have a passenger car on the end of a freight to simulate a business car with company brass. K-Line made some nice business cars, or you could use any open platform observation car or solarium.