Maxing 3 times a week for squats isn't a bad idea, I did it in the past and it worked out great. (I hope you already considered de-loading/resting weeks at least once every 4-6 weeks)
With that being said, maxing 3 times a week on the bench press ALONG squats?

Not a good idea
Did heavy squating 3 times a week aswell, untill I reached point where it got really heavy. Then my knee joints started hurting. Should have deloaded more i suppose and perhaps change rep schemes a bit. ^_^
@Fabbe: You could do chest 3 times a week in my opinnion, just not as heavy as you are planning. If you wishes to bench 3x a week, you could add some changing variables such as: Decline bench, incline bench, DB bench or even chest dips. Use light/medium weights once or twice a week and go heavy once or twice.
You could also switch the first exercise for each day to ensure that all muscles improve in quite equal manner.
Day 1:
Squats - work up to a max + back off sets
Bench press - Medium rep scheme 3x8 with apropriate weights.
Deadlift - 1x5
Weighted dips 3x3-5
Day 3:
Bench work up to 2 max effort sets + back off sets
Underhand BB rows 3x3-5
Squats - Light/medium weights with rep scheme off: 3x8 or 3x12-15, or even 2x20.
Core work* (?)
Day 4:
Deadlift 5x1 (Work in 83-90% of 1RM)
Bench press - Light weights with rep scheme: 3x12-15 or 2x20.
Squats - work up to a max + back off sets
Weighted dips 3x3-5
Eitherway that's just my 5 cents.