This paper proposes and analyzes the performance of the multihop free-space optical (FSO) communication links using a heterodyne differential phase-shift keying modulation scheme operating over a turbulence induced fading channel. A novel statistical fading channel model for multihop FSO systems using channel-state-information-assisted and fixed-gain relays is developed incorporating the atmospheric turbulence, pointing errors, and path-loss effects. The closed-form expressions for the moment generating function, probability density function, and cumulative distribution function of the multihop FSO channel are derived using Meijer's G-function. They are then used to derive the fundamental limits of the outage probability and average symbol error rate. Results confirm the performance loss as a function of the number of hops. Effects of the turbulence strength varying from weak-to-moderate and moderate-to-strong turbulence, geometric loss, and pointing errors are studied. The pointing errors can be mitigated by widening the beam at the expense of the received power level, whereas narrowing the beam can reduce the geometric loss at the cost of increased misalignment effects.