We present GASPACHO: a method for generating photorealistic controllable renderings of human-object interactions. Given a set of multi-view RGB images of human-object interactions, our method reconstructs animatable templates of the human and object as separate sets of Gaussians simultaneously. Different from existing work, which focuses on human reconstruction and ignores objects as background, our method explicitly reconstructs both humans and objects, thereby allowing for controllable renderings of novel human object interactions in different poses from novel-camera viewpoints. During reconstruction, we constrain the Gaussians that generate rendered images to be a linear function of a set of canonical Gaussians. By simply changing the parameters of the linear deformation functions after training, our method can generate renderings of novel human-object interaction in novel poses from novel camera viewpoints. We learn the 3D Gaussian properties of the canonical Gaussians on the underlying 2D manifold of the canonical human and object templates. This in turns requires a canonical object template with a fixed UV unwrapping. To define such an object template, we use a feature based representation to track the object across the multi-view sequence. We further propose an occlusion aware photometric loss that allows for reconstructions under significant occlusions. Several experiments on two human-object datasets - BEHAVE and DNA-Rendering - demonstrate that our method allows for high-quality reconstruction of human and object templates under significant occlusion and the synthesis of controllable renderings of novel human-object interactions in novel human poses from novel camera views.