Existing audio-score alignment methods assume that the audio performance is faithful to a fully-notated MIDI score. For semi-improvised music (e.g. jazz), this assumption is strongly violated. In this paper, we address the problem of aligning semi-improvised music audio with a lead sheet. Our approach does not require prior training on performances of the lead sheet to be aligned. We start by analyzing the problem and propose to represent the lead sheet as a MIDI file together with a structural information file. Then we propose a dynamic-programming-based system to align the chromagram representations of the audio performance and the MIDI score. Techniques are proposed to address the chromagram scaling, key transposition and structural change (e.g. a performer unexpectedly repeats a section) problems. We test our system on 3 jazz lead sheets. For each sheet we align a set of solo piano performances and a set of fullband commercial recordings with different instrumentation and styles. Results show that our system achieves promising results on some highly improvised music.