An elastic laminate that contains a nonwoven web bonded to an elastic layer is provided. The elastic layer contains one or more elastomeric polymers that are generally polar in nature, such as polyurethanes. To the contrary, the nonwoven web is formed from a material that is non-polar in nature. Nevertheless, one or more surfaces of the nonwoven web are fluorinated so that the resulting surface tension is increased. In this manner, the present inventors have discovered that, despite the difference in polarity between the layers, good attachment may be achieved without necessarily requiring an adhesive. Not only will such layers remained attached, but the functionality of the resulting laminate is also not adversely affected.