Obstructions such as raindrops, fences, or dust degrade captured images, especially when mechanical cleaning is infeasible. Conventional solutions to obstructions rely on a bulky compound optics array or computational inpainting, which compromise compactness or fidelity. Metalenses composed of subwavelength meta-atoms promise compact imaging, but simultaneous achievement of broadband and obstruction-free imaging remains a challenge, since a metalens that images distant scenes across a broadband spectrum cannot properly defocus near-depth occlusions. Here, we introduce a learned split-spectrum metalens that enables broadband obstruction-free imaging. Our approach divides the spectrum of each RGB channel into pass and stop bands with multi-band spectral filtering and learns the metalens to focus light from far objects through pass bands, while filtering focused near-depth light through stop bands. This optical signal is further enhanced using a neural network. Our learned split-spectrum metalens achieves broadband and obstruction-free imaging with relative PSNR gains of 32.29% and improves object detection and semantic segmentation accuracies with absolute gains of +13.54% mAP, +48.45% IoU, and +20.35% mIoU over a conventional hyperbolic design. This promises robust obstruction-free sensing and vision for space-constrained systems, such as mobile robots, drones, and endoscopes.