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The book was available in paperback, and published around the 1981- late 1984 timeframe.

The plot revolves around a lower-cost way to launch shuttles with a re-usable carrier aircraft underneath it. The carrier aircraft is supersonic or hypersonic, power by scramjet or perhaps pure rocket engines.

The launcher aircraft gets the Space Shuttle into a the upper atmosphere, where it can fire its main engines and press into low-earth orbit.

A malfunction prevents the carrier ship from detaching from the shuttle, and the carrier ship pilots are in danger since their ship wasn't designed for a space mission.

Details are fuzzy after that.

This sounds like a book called "Shuttle" written by David C Onley and published in 1981.

Edwards Air Force Base: the giant Hypersonic Jet Yorktown with the Shuttle Columbia clasped to her back, climbs to the sky. Their pioneering mission: to launch the Shuttle into space from the edge of the atmosphere. Neither craft will reach its destination. One will never return. Fact and fiction combine in this dramatic, bestselling novel of a space shuttle mission that goes perilously wrong. With the shattered craft locked in fatal orbit, their crew running a desperate race against time, Mission Control mounts a last ditch effort that must not fail. The result is a stunning story of rescue is space that grips to the very last page.

I know I had it at one point, just had a quick look but can't find it.