The frequency cross-spectrum for intensity fluctuations arising in a wave that has traversed a deeply modulated phase-changing screen is investigated in the case when the incident wave field is nonmonochromatic. An analytic expression is obtained for this spectrum and compared with the results of a direct numerical integration of the initial integral expression. The effect of increasing frequency differences is demonstrated. Finally, by comparing second and fourth moments in the far field, it is shown that while the assumption of joint normal statistics is valid in this region for a monochromatic wave field it breaks down for non-monochromatic fields. Thus wave fields of different frequencies scattered by a deeply modulated phase-changing screen do not have a joint normal distribution in the far field.