Multispectral photoacoustic tomography (PAT) is capable of resolving tissue chromophore distribution based on spectral un-mixing. It works by identifying the absorption spectrum variations from a sequence of photoacoustic images acquired at multiple illumination wavelengths. Due to multispectral acquisition, this inevitably creates a large dataset. To cut down the data volume, sparse sampling methods that reduce the number of detectors have been developed. However, image reconstruction of sparse sampling PAT is challenging because of insufficient angular coverage. During spectral un-mixing, these inaccurate reconstructions will further amplify imaging artefacts and contaminate the results. To solve this problem, we present the interlaced sparse sampling (ISS) PAT, a method that involved: 1) a novel scanning-based image acquisition scheme in which the sparse detector array rotates while switching illumination wavelength, such that a dense angular coverage could be achieved by using only a few detectors; and 2) a corresponding image reconstruction algorithm that makes use of an anatomical prior image created from the ISS strategy to guide PAT image computation. Reconstructed from the signals acquired at different wavelengths (angles), this self-generated prior image fuses multispectral and angular information, and thus has rich anatomical features and minimum artefacts. A specialized iterative imaging model that effectively incorporates this anatomical prior image into the reconstruction process is also developed. Simulation, phantom, and in vivo animal experiments showed that even under 1/6 or 1/8 sparse sampling rate, our method achieved comparable image reconstruction and spectral un-mixing results to those obtained by conventional dense sampling method.