We report an InP-InGaAs-InP double heterojunction bipolar transistor (DHBT), fabricated using a conventional triple mesa structure, exhibiting a 370-GHz f(t) and 459-GHz f(max), which is to our knowledge the highest f(tau)reported for a mesa InP DHBT--as well as the highest simultaneous f(t) and f(max) for any mesa HBT. The collector semiconductor was undercut to reduce the base-collector capacitance, producing a Ccb/Ic ratio of 0.28 ps/V at Vcb = 0.5 V. The BV,CEO is 5.6 V and the devices fail thermally only at > 18 mW/um^2, allowing dc bias from J(e) = 4.8 mA/um^2 at Vce = 3.9 V to J(e) = 12.5 mA/um^2 at Vce = 1.5 V. The device employs a 30 nm carbon-doped InGaAs base with graded base doping, and an InGaAs-InAlAs superlattice grade in the base-collector junction that contributes to a total depleted collector thickness of 150 nm.