Identifying different protein compositions and conformations from microscopic images of protein mixtures is a challenging open problem. We address this problem through disentangled representation learning, where separating protein compositions and conformations in an intermediate latent space enables accurate identification. Since conformations manifest as transformations that cause subtle changes in voxel space and compositions correspond to content invariant to these transformations, the task reduces to content-transformation disentangling. However, existing content-transformation disentanglement methods require an explicit parametric form for the transformation, which conformation transformations lack, making those methods unsuitable. To overcome this limitation, we propose DualContrast, a novel contrastive learning-based method that implicitly parameterizes both transformation and content and disentangles them. DualContrast achieves this by generating positive and negative pairs for content and transformation in both data and latent spaces. We demonstrate that existing contrastive approaches fail under similar implicit parameterization, underscoring the necessity of our method. We validate our claims through extensive experiments on 3D microscopic images of protein mixtures and additional shape-focused datasets beyond microscopy. Finally, we achieve the first completely unsupervised identification of different protein compositions and conformations in 3D microscopic images of protein mixtures.