Curriculum learning helps language models tackle complex reasoning by gradually increasing task difficulty. However, it often fails to generate consistent step-by-step reasoning, especially in multilingual and low-resource settings where cross-lingual transfer from English to Indian languages remains limited.We propose IRIS: Interleaved Reinforcement with Incremental Staged Curriculum, a two-axis framework that combines Supervised Fine-Tuning on progressively harder problems (vertical axis) with Reverse Curriculum Reinforcement Learning to reduce reliance on step-by-step guidance (horizontal axis). We design a composite reward combining correctness, step-wise alignment, continuity, and numeric incentives, optimized via Group Relative Policy Optimization (GRPO). We release CL-Math, a dataset of 29k problems with step-level annotations in English, Hindi, and Marathi.Across standard benchmarks and curated multilingual test sets, IRIS consistently improves performance, with strong results on math reasoning tasks and substantial gains in low-resource and bilingual settings, alongside modest improvements in high-resource languages. Our code and dataset will be publicly available at https://github.com/avinanand/IRIS-Interleaved-Reinforcement-