In this paper, we discuss the problem of instantaneous frequency (IF) estimation of phase signals using their level-crossing (LC) instant information. We cast the problem to that of interpolating the instantaneous phase (IP), and hence finding the IF, from samples obtained at the level-crossing instants of the phase signal. These are inherently irregularly spaced and the problem essentially reduces to reconstructing a signal from the samples taken at irregularly sampled points for which we propose a ‘line plus sum of sines’ model. In the presence of noise, the temporal structure of the level-crossings can get distorted. To reduce the effects of noise, we use a short-time Fourier transform (STFT) based enhancement scheme. The performance of the proposed method is studied through Monte-Carlo simulations for a phase signal with composite IF for various SNRs. Different level-crossing based estimates are combined to obtain a new IFestimate. Simulation studies show that the estimates obtained using zero-crossing (ZC) and other very low level values perform better than those obtained with higher level values.