We report the growth and device characterization of InAlAs/InGaAs/InP double-heterojunction bipolar transistors in a solid source molecular beam epitaxy system with a valved-phosphorus cracker. Linearly graded InGaAlAs base-collector and emitter-base junctions were used. Photoreflectance characterization shows excellent growth reproducibility. The dc current-voltage characteristics of a 1.5x10 mu m(2) device indicate high breakdown voltage, low offset voltage, and good linearity. Breakdown voltage of an InP-collector device with compositionally graded base-collector junction is 19 V compared to 11 V for an InGaAs-collector device. By comparison, a chirped superlattice base-collector junction shows significant current oscillations due to the carrier tunneling effect. High-frequency performance was similar to previously reported InGaAs-collector devices; unity current-gain frequency and unity maximum-available power gain frequency are 75 and 140 GHz, respectively.