Recently, there has been an interest in the incorporation of buckypaper (BP), or carbon nanotube (CNT) membranes, in composite laminates. Research has shown that using BP in contrast to nanotube doped resin enables the introduction of a higher CNT weight fraction which offers multiple benefits including higher piezo resistivity for health monitoring applications and enhanced mechanical response for structural applications. However, their impact on the deformation and failure mechanisms of composite laminates has not been investigated thoroughly. Understanding these issues experimentally would require a carefully executed test plan involving a multitude of design parameters such as BP geometry and placement, material anisotropy and variability, and laminate stacking sequence. This paper presents a deep learning (DL)-based surrogate model for studying the mechanical response of hybrid carbon fiber reinforced polymer (CFRP) composite laminates with BP interleaves under various mechanical loads. The surrogate model utilizes a long short-term memory architecture implemented within a DL framework and predicts the laminate global response for a given configuration, geometry, and loading condition. The DL framework training and cross-validation are performed via data acquisition from a series of three-point bend tests conducted through finite element analysis (FEA) and in-house experiments, respectively. The model predictions show good agreement with FEA simulations and experimental results, where CFRP with two BP interleaves showed enhanced flexural strength and modulus over pristine samples. This enhancement can be attributed to the excellent crack retardation capabilities of CNTs, particularly in the interlaminar region.