Contrastive language-audio pre-training (CLAP), which learns audio-language representations by aligning audio and text in a common feature space, has become popular for solving audio tasks. However, CLAP's audio features lack generalizability, whereas self-supervised learning (SSL) models offer general-purpose features that perform well across diverse audio tasks. We aim to develop a broadly applicable audio representation and hypothesize that a model that learns both general audio and CLAP features should achieve our goal, which we call a general-purpose audio-language representation. To implement our hypothesis, we propose M2D-CLAP, the first approach to jointly learn effective general audio and CLAP features. It extends an SSL masked modeling duo (M2D) by incorporating CLAP and utilizes LLM-based sentence embeddings. The training process consists of multiple stages. In the first stage, generalizable audio features are pre-trained via a multitask objective combining M2D and CLAP, with CLAP leveraging LLM-based semantic embeddings to distill semantic knowledge into them. In the following stages, CLAP features are pre-trained and refined with guidance from the learned audio features. Experiments demonstrated that M2D-CLAP learns high-performing general audio features (e.g., AudioSet mAP of 49.0, SOTA results in music tasks) and CLAP features, thereby enabling a general-purpose audio-language representation.