Fiber-reinforced thermoplastic composites fabricated by filament-based multi-axis 3D printing offer high strength-to-weight ratios, yet their highly anisotropic failure behavior makes performance extremely sensitive to the interaction among structural topology, layer sequencing, and deposition orientations. Existing workflows often adopt a two-stage strategy: optimizing structural layouts first, then generating manufacturable curved layers and tool motions afterward. This separation can force compromises, reducing achievable strength once collision avoidance, motion DoFs, and thickness limits are enforced. Recent neural approaches such as Neural Slicer for multi-axis curved-layer generation [2] and neural co-optimization pipelines for composite printing [1] indicate the potential of implicit representations. We propose a neural network-based computational framework for the simultaneous optimization of structural topology, curved layers, and path orientations to achieve strong anisotropic strength in fiber-reinforced thermoplastic composites while ensuring manufacturability. Our framework employs three implicit neural fields to represent geometric shape, layer sequence, and fiber orientation, enabling continuous queries and an integrated differentiable optimization. This representation supports the direct formulation of both design and manufacturability objectives—including anisotropic strength under an orthotropic yield criterion [3], structural volume control in density-based topology optimization [4], and printing constraints such as machine motion control, layer curvature regularization for collision-free deposition, and bounded layer thickness via gradient-based thickness control. By incorporating these objectives as loss functions and optimizing end-to-end with gradient-based learning [5], the framework yields composites that are mechanically optimized yet directly printable across hardware platforms with different motion DoFs. Physical experiments demonstrate that composites produced by our co-optimization method achieve up to 33.1% improvement in failure loads compared to sequentially optimized structures and manufacturing sequences, and further comparisons across 5-axis, 3-axis, and 2.5-axis settings validate that our unified formulation consistently adapts to different motion DoFs while maintaining printability and strength gains.