This work proposes a multi-phase field method relying on the PUCK failure criteria for triggering the fracture in fiber and the inter-fiber (matrix-dominated) separately, using two independent phase-field damage variables in a thermodynamically consistent framework. Furthermore, the formulation encompasses two distinct characteristic length scales, and a structural tensor is employed to penalize the gradient of the phase field, enhancing the accuracy of qualitative and quantitative predictions. The proposed model accommodates various failure modes that align with the PUCK failure theory. Furthermore, Puck failure theory is used for crack initiation, while the phase field method is used for crack propagation. The driving force stemming from the energy of the fiber and matrix is coupled with the Puck failure theory. The model's predictive capabilities are examined using single-ply and multi-ply laminates of different plies and crack tip geometries orientations. Laminates of layup sequence such as $ [(45^{\circ}/-45^{\circ})_8]_s$, $ [(60^{\circ}/-60^{\circ})_8]_s$ without a preexisting notch are used to demonstrate the capability of the model to handle both tension and compression. Furthermore, examples such as open-hole tension and compact tension of various laminate sequences are used to compare with the experimental results and showcase the model's ability to replicate the experiment results. As an example, Fig 1. shows the comparison for an open hole tension specimen for the layup sequence of $ [(45^{\circ}_4/-45^{\circ}_4)]_s$. The crack initiation and propagation stemming from the model are compared to the experimental observations [1] in Fig 1.