If you do the research, you should discover that the application of a wood mulch does no more to attract termites than does leaving the soil bare or using a rock mulch. And some types of mulches do tend to discourage insects period, due to high tanins and pungent essential oils the insects find disagreeable.

Mulching is really the most effective method of weed control. Just keep any wood mulch several inches away from the side of your house or any wooden surfaces - a border of coarse gravel right next to the house is effective and since this is typically an area that receives minimal sunlight and is protected from rain by eaves, not all that desireable for either plantings or weeds.

Here is a link that might be useful: the truth about termites and mulch