Nonverbal vocalizations (NVVs), such as laughing, sighing, and sobbing, are essential for human-like speech, yet standardized evaluation rarely jointly assesses whether systems generate the intended NVVs, place them correctly, and keep them salient without harming speech. We present NVV-SuperBench, a bilingual English/Chinese benchmark for speech generation with NVVs. It provides a unified 45-type taxonomy and a multi-axis protocol beyond conventional speech quality assessment, evaluating NVV-specific controllability, placement, and perceptual salience. We benchmark 15 speech generation systems spanning prompt-based and tag-based control paradigms, using objective metrics, human listening tests, and LLM-based multi-rater evaluation. Results show that NVV controllability often decouples from speech quality, while low-SNR oral cues and long-duration affective NVVs remain bottlenecks. NVV-SuperBench highlights current gaps and supports progress toward more human-like speech generation.