If you only care about the date
var firstDay = new DateTime(date.Year, date.Month, 1, 0, 0, 0, date.Kind);
var lastDay = new DateTime(date.Year, date.Month, 1, 0, 0, 0, date.Kind).AddMonths(1).AddDays(-1);
If you want to preserve time
var firstDay = new DateTime(date.Year, date.Month, 1, date.Hour, date.Minute, date.Second, date.Kind);
var lastDay = new DateTime(date.Year, date.Month, 1, date.Hour, date.Minute, date.Second, date.Kind).AddMonths(1).AddDays(-1);