Depthwise and pointwise convolutions have fewer parameters and perform fewer operations than standard convolutions. As a result, they have become increasingly used in various compact DNNs, including convolutional neural networks (CNNs) and vision transformers (ViTs). However, they have a lower compute-to-memory-access ratio than standard convolutions, making their memory accesses often the performance bottleneck. This paper explores fusing depthwise and pointwise convolutions to overcome the memory access bottleneck. The focus is on fusing these operators on GPUs. The prior art on GPU-based fusion suffers from one or more of the following: (1) fusing either a convolution with an element-wise or multiple non-convolutional operators, (2) not explicitly optimizing for memory accesses, (3) not supporting depthwise convolutions. This paper proposes Fused Convolutional Modules (FCMs), a set of novel fused depthwise and pointwise GPU kernels. FCMs significantly reduce pointwise and depthwise convolutions memory accesses, improving execution time and energy efficiency. To evaluate the trade-offs associated with fusion and determine which convolutions are beneficial to fuse and the optimal FCM parameters, we propose FusePlanner. FusePlanner consists of cost models to estimate the memory accesses of depthwise, pointwise, and FCM kernels given GPU characteristics. Our experiments on three GPUs using representative CNNs and ViTs demonstrate that FCMs save up to 83\% of the memory accesses and achieve speedups of up to 3.7x compared to cuDNN. Complete model implementations of various CNNs using our modules outperform TVMs' achieving speedups of up to 1.8x and saving up to two-thirds of the energy. FCM and FusePlanner implementations are open source: https://github.com/fqararyah/Fusing_DW_and_PW_on_GPUs.