Fully Homomorphic Encryption (FHE) enables computation on encrypted data and is promising for privacy-preserving computing. However, FHE deployment remains constrained due to massive computational, memory, and data-movement overheads. Existing acceleration strategies often overlook the storage I/O bottleneck caused by the enormous size of FHE data in large-scale applications, as most prior works focus on small benchmarks that fit in main memory. Our studies show that state-of-the-art FHE systems spend 71\% to 85\% of their execution time moving data between storage and compute units rather than performing useful computation. To address the I/O bottleneck, we present Rosemary, a heterogeneous FHE acceleration system that incorporates a novel in-storage processing (ISP) architecture with compiler-level and algorithmic optimizations. Our key innovations include 1) an adaptable hardware-aware FHE engine inside a NAND flash-based solid-state drive (SSD) for efficient and cost-effective in-storage FHE processing, 2) a Throughput-Data-Aware Program Allocator (TDAP) that partitions FHE workloads into heterogeneous programs, and 3) a Compiler-Level Ciphertext-Aware Optimizer (CLCAO) that exploits ISP-friendly FHE kernels for low-cost ISP execution. Across a diverse set of FHE workloads, including encrypted deep learning inference and cloud database queries, Rosemary achieves geometric-mean speedups of $185.7\times$ over state-of-the-art CPU/GPU implementations and $3.7\times$ over prior FHE accelerators, while improving energy efficiency by up to $3.9\times$ and Energy-Delay-Area-Product (EDAP) by up to $16.5\times$.

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