Current speech encoding pipelines often rely on an additional text-based LM to get robust representations of human communication, even though SotA speech-to-text models often have a LM within. This work proposes an approach to improve the LM within an audio model such that the subsequent text-LM is unnecessary. We introduce WhiSPA (Whisper with Semantic and Psychological Alignment), which leverages a novel audio training objective: contrastive loss with a language model embedding as a teacher. Using over 500k speech segments from mental health audio interviews, we evaluate the utility of aligning Whisper's latent space with semantic representations from a text autoencoder (SBERT) and lexically derived embeddings of basic psychological dimensions: emotion and personality. Over self-supervised affective tasks and downstream psychological tasks, WhiSPA surpasses current speech encoders, achieving an average error reduction of 73.4% and 83.8%, respectively. WhiSPA demonstrates that it is not always necessary to run a subsequent text LM on speech-to-text output in order to get a rich psychological representation of human communication.