We propose and experimentally demonstrate a stable homodyne phase demodulation technique in a ϕ-OTDR using a double-pulse probe and a simple direct detection receiver. The technique uses selective phase modulation of one of a pair of pulses to generate a carrier for dynamic phase changes and involves an enhanced phase demodulation scheme suitable for distributed sensing by being robust against light intensity fluctuations, independent of the modulation depth, and convenient for analogue signal processing. The capability of the technique to quantify distributed dynamic phase change due to a generic external impact is experimentally demonstrated by measuring the phase change induced by a nonlinear actuator generating a 2 kHz perturbation at a distance of 1.5 km on a standard singlemode fiber with an SNR of ~24 dB. The demodulated nonlinear response is shown to have a spectrum consistent with one obtained using an FBG sensor and a commercial reading unit.