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Recently, a lot of automated white blood cells (WBC) or leukocyte classification techniques have been developed. However, all of these methods only utilize a single modality microscopic image i.e. either blood smear or fluorescence based, thus missing the potential of a better learning from multimodal images. In this work, we develop an efficient multimodal architecture based on a first of its kind multimodal WBC dataset for the task of WBC classification. Specifically, our proposed idea is developed in two steps - 1) First, we learn modality specific independent subnetworks inside a single network only; 2) We further enhance the learning capability of the independent subnetworks by distilling knowledge from high complexity independent teacher networks. With this, our proposed framework can achieve a high performance while maintaining low complexity for a multimodal dataset. Our unique contribution is two-fold - 1) We present a first of its kind multimodal WBC dataset for WBC classification; 2) We develop a high performing multimodal architecture which is also efficient and low in complexity at the same time.