The aim of the present work is to develop modeling strategies by means of advanced constitutive models and computational frameworks for describing the mechanical behavior of hyperelastic fiber-reinforced materials undergoing finite deformations while being proposed for high efficiency and robustness in finite element application. A unified invariant-base model in terms of the general deformation invariants is proposed to account the contributions of the individual constituent materials, i.e. soft matrix and fibers, and particularly their matrix-fiber mechanical interactions. The present study represents an initial attempt to model matrix-fiber interface debonding in the context of pseudo-elasticity and, moreover, to characterize and computationally evaluate it. For this, inelastic phenomena such as discontinuous Mullins-type softening and permanent set as a result of the matrix damage, the fiber rupture, and the matrix-fiber interface debonding are modeled. The proposed elastic and inelastic constitutive models are successfully implemented into a finite element environment through a general user-defined interface to study a range of initial boundary value problems. Distinct and particular contributions of the matrix, the fibers, and the matrix-fiber mechanical interaction as well as their respective damage counterparts are characterized independently through performing a comprehensive set of cyclic tensile tests. The experimental observations indicate that fiber-reinforced soft composites exhibit rich complexities, such as nonlinearity, anisotropy, Mullins type softening, and permanent deformations. This work bridges the degradation of the mechanical properties to the microscopically visible matrix-fiber interface debonding for composites undergoing cyclic deformations. The conformability of the invariant-based constitutive model, implemented in the user-defined subroutine, is validated against the experimental data of composites with different material anisotropy, indicating good qualitative agreements. Moreover, the pseudo-elastic model is verified by comparison to the cyclic tensile tests, showing a reasonable range of agreement. Finally, this study identifies a unique performance benefit in flexible composite laminates through evaluation of the load-coupling potentials once an external stimulus triggers extensional loadings. To this end, the exceptional, tunable flexibilities of the material are exploited to build up composite laminates with different ply thicknesses, stacking directions, constituent materials, and numbers of plies. A design space is then introduced and used to evaluate the capability of laminates for effective load-coupling behaviors.