We present a jump-diffusion stochastic differential equation model for all-India monthly rainfall anomalies from 1901 to 2021, which captures both continuous mean-reverting variability and discrete heavy-rain "jumps." Seasonal cycles are removed to obtain anomalies Ai, with the top 5% of values identified as Poisson-driven jumps at a rate of 0.605 events per year. Jump sizes follow a Gamma distribution (α = 20.24, θ = 2.84), while non-jump increments exhibit linear drift a(R) = 0.123 + 0.877R and diffusion σ = 23.59 mm month-1/2. Simulations reproduce observed dynamics, and sliding-window analysis reveals slight long-term declines in jump frequency and volatility. Return-level analysis yields 10-year and 100-year anomalies of 69.8 mm and 88.0 mm, respectively, and exceedance probabilities are quantified for various horizons. This framework offers actionable metrics for water-resource planning, flood risk management, and insurance applications.