This paper proposes a novel, to the best of our knowledge, double-image hiding scheme based on the chaotic fingerprint phase masks (CFPMs) and three-step phase-shifting digital holography (PSDH). First, the two images to be hidden are encoded into a complex amplitude image, and then with the help of the CFPM located in the Fresnel transform (FrT) domain and the three-step PSDH, the complex amplitude image can be encoded into three noise-like interference holograms. Finally, the three noise-like interference holograms are hidden into the texture part of the host image by the discrete wavelet transform based fusion approach and variational image decomposition technique. This scheme can simultaneously hide two images into one host image, and the invisibility and robustness of the hiding scheme can be well balanced by embedding the secret image in the texture of the host image. Additionally, the introduction of a biometric feature increases the association of the key and the authorized user, and the parameters of the chaotic map and FrT can also provide additional security to the proposed scheme. We have verified the scheme's feasibility, security, and robustness through extensive experiments.