Recently, multiple‐shape memory polymers (SMPs) have attracted a great deal of attention in biomedical applications. Therefore, a series of triple‐SMPs were developed by simply blending of two immiscible SMPs exhibiting two distinct transition temperatures, which is required for triple‐shape memory (SM) effect. However, fabrication of triple‐SMPs from completely miscible polymer pairs using the conventional blending approach is a challenging problem. Because this type of blends consists of one homogeneous phase and thereby exhibit only one transition temperature and dual‐SM behavior. To overcome this problem, herein, a novel and versatile strategy is introduced for preparation of phase separated blends from a completely miscible polymer pair, exhibiting triple‐SM behavior. Dual‐electrospinning technique was utilized to simultaneously electrospin poly(lactic acid) (PLA) and poly(vinyl acetate) (PVAc), as a model miscible polymer pair, to obtain an interwoven polymer composite with two well‐separated thermal transitions, as revealed by dynamic mechanical analyze. Consequently, the SM experiments revealed that the electrospun PLA/PVAc composites have triple‐SM behavior. Furthermore, incorporation of graphene nanoplatelets into the composite fibers significantly improved the triple‐SM properties of samples. Additionally, excellent adherence and spreading of the osteoblasts on the fibrous scaffolds containing graphene were observed. © 2019 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2019, 136, 47471.