The adults of beetles called June bugs (more accurately called June beetles) have very weak mouthparts and rarely feed on anything, so I think you are dealing with a different pest.  The adult of European chafer beetles look quite a bit like June beetles, but are smaller and a bit lighter colored.  These are active at night and do feed on many plants.  The immature stages of the European chafer are grubs in the soil, usually feeding on the roots of turf grasses.  They are susceptible to the same nematodes that are sold for use against June beetles and Japanese beetles.  The success of treating with nematodes varies greatly, they are very frail organisms which require exacting conditions for storage, shipping, and application.  European chafers can be controlled fairly well with a single, well times application of a lawn grub control pesticide product (product offerings vary greatly, you'll have to see what is available locally).  The best time for an application is just after the adults deposit their eggs, usually around the beginning of August.  A fall application can be somewhat effective, but it should be made before we get into really cold weather. 

Like Japanese beetles and June beetles, the adults of the European chafer can fly and travel a good distance in one evening, so even if you could control them well in your own lawn there might still be a lot of plant injury from beetles flying in from other places.