We demonstrate a high-sensitivity acetylene/methane gas sensor based on hollow-core fiber photothermal interferometry (PTI) with a pump-probe-alternating technique. This technique utilizes two distributed-feedback lasers as pump and probe beams alternatively for two gas components to facilitate photothermal phase modulation and detection through time-division multiplexing. With a 2.5-cm-long hollow-core conjoint-tube fiber, noise-equivalent concentrations of 370 ppb and 130 ppb are demonstrated for methane and acetylene, respectively. Noise characteristics of the PTI system are analyzed and experimentally tested. The proposed technique eliminates the need for an additional laser in the traditional PTI setup, enabling the construction of a sensitive yet more cost-effective multi-gas component detection system.