The low thickness of plastic films poses a challenge when using near-infrared (NIR) spectroscopy as it affects the spectral quality and classification. This research focuses on offering a solution to the challenge of classifying multilayer plastic film materials with a focus on polyolefin multilayer plastics. It presents the importance of spectral quality on accurate classification. The aim is to demonstrate the suitability of the handheld NIR spectrometer in classifying multilayer polyolefin films and assess the impact of various measuring backgrounds (white tile, Teflon, aluminum, copper, silver, and gold) on classification accuracy in the wavelength range of 1596–2396 nm. Metallic backgrounds have been found to enhance spectral quality and classification accuracy. The classification accuracy was consistently high, ranging from 96.55% to 100%, with aluminum and gold backgrounds yielding the best results in theoretical accuracy. In experimental classification, the accuracy reached 100% when any metallic backgrounds were used. Conversely, Teflon showed a theoretically high accuracy of 96.21% but only achieved an experimental accuracy of 72.2%. These findings suggest that using metallic backgrounds can improve the spectral quality and classification of plastics with low thickness (films) and complex material composition (multilayers).