Due to the development of pre-trained language models, automated code generation techniques have shown great promise in recent years. However, the generated code is difficult to meet the syntactic constraints of the target language, especially in the case of Turducken-style code, where declarative code snippets are embedded within imperative programs. In this study, we summarize the lack of syntactic constraints into three significant challenges: (1) the efficient representation of syntactic constraints, (2) the effective integration of syntactic information, and (3) the scalable syntax-first decoding algorithm. To address these challenges, we propose a syntax-guided multi-task learning approach TurduckenGen. Specifically, we first explicitly append the type information to the code tokens to capture the representation of syntactic constraints. Then we formalize code generation with syntactic constraint representation as an auxiliary task to enable the model to learn the syntactic constraints of the code. Finally, the syntactically correct code is selected accurately from the multiple candidates with the help of the compiler feedback. Extensive experiments and comprehensive analysis demonstrate the effectiveness and general applicability of our approach after being compared with six state-of-the-art baselines on two Turducken-style code datasets. Finally, we conducted a human study and found the code quality generated by our approach is better than baselines in terms of code readability and semantic similarity.