In this paper we develop a finite deformation micromechanical framework for modeling rate-dependent failure in unidirectional composites under off-axis loading. The model performance is compared with original experiments on thermoplastic carbon/PEEK composites tested at different strain-rates and off-axis angles. To achieve quantitative agreement with the experiments, a microcrack initiation criterion based on the local stress and the local rate of deformation state in the polymer matrix is proposed. Microcracking is represented by a cohesive zone model, with special attention to the inclusion of geometric nonlinearity in the formulation. In this regard, the cohesive geometric nonlinearity is based on extension of an existing formulation to three-dimensional space. Beside microcracking, the Representative Volume Element (RVE) also accounts for viscoplasticity in the polymer matrix. A recently introduced dedicated arclength control method is utilized to impose a strain-rate on the micromodel. Accordingly, kinematic relations governing the RVE deformation allow for the change in orientation of the micromodel in the loading process. This change in orientation of the microstructure has an important implication on the apparent material strength.