Unsupervised domain adaptation using adversarial learning has shown promise in adapting speech models from a labeled source domain to an unlabeled target domain. However, prior works make a strong assumption that the label spaces of source and target domains are identical, which can be easily violated in real-world conditions. We present AMLS, an end-to-end architecture that performs Adaptation under Mismatched Label Spaces using two weighting schemes to separate shared and private classes in each domain. An evaluation on three speech adaptation tasks, namely gender, microphone, and emotion adaptation, shows that AMLS provides significant accuracy gains over baselines used in speech and vision adaptation tasks. Our contribution paves the way for applying UDA to speech models in unconstrained settings with no assumptions on the source and target label spaces.