Remote sensing acquisition systems rely on a range of platforms, from drones to satellite missions, to record multimodal Earth surface data. This fact encourages the preparation of datasets with complementary properties, thereby increasing their discriminative potential. A common complementary combination is between Hyperspectral and LiDAR-generated digital surface model data. While engaging, this fusion poses challenges for specific applications. Multiple works fuse these modalities at the feature level using vector concatenation, maximization, or averaging. Although functional, these methods omit target interactions between the modalities. Another challenge in remote sensing is the quantity and quality of labels required by deep learning methods, which are expensive, error-prone, and difficult to scale. We address the challenges above by proposing a self-supervised processing framework based on cross-modal attention that effectively fuses features at multiple levels, thereby exploiting complementary information across data streams. Specifically, our method is founded on a pseudo-Siamese network that reweights each modality’s features with information from the other via a mirrored cross-modal attention. The network’s objective is to maximize the similarity between the feature representations of both streams. A fusion network builds a latent representation using the learned encoders and attention modules. Then, a k-Nearest Neighbor classifier categorizes each sample within the representation using ten labels per class. Our experiments show that our spatial- and channel-spatial cross-modal attention approaches outperform well-established fusion methods for label-efficient land cover classification across datasets. Our findings lay the groundwork for fusion methods that effectively exploit inter-stream data relationships to encourage complementarity.