The paper introduces a cubic-phase-function based method to estimate interference phase in digital holographic interferometry. The proposed method relies on piecewise polynomial approximation of phase by dividing an arbitrary row/column of the complex reconstructed interference field in many segments and modeling signal data in each segment as a cubic phase signal. The polynomial coefficients in each segment are determined using cubic phase function algorithm. The phase is subsequently evaluated from the polynomial constructed using the obtained polynomial coefficients. The piecewise polynomial approximation approach is extended for all rows/columns and the overall phase is thus determined. The method's applicability is demonstrated using simulation and experimental results.