It won't work in most cases
I have tried to do this before--a mix of business & econ on a same ticket. It doesn't work if on the economy leg, there is a business class cabin available. It books into the same class--eithe rall economy or all business.
However, certain travel agents or consolidators may be able to do it. I have even called the airlines themselves, and they cannot do it. But I know that some travel agents can do it.
The othe alternative is to simply book separate itineraries--long hauls in business and shorthauls in economy. The problem with that, however, is the luggage. You can ask at the airport for the person to check you in all the way through, but sometimes you have to retrieve your luggage and re-check it in because it's a different itinerary. However, with the new bar-code luggage tags, they usually can check you in all the way through, even on a different airline.