You can use LINQ to find this consider the following code:
string StartDate="3/15/2015";
string EndDate = "5/6/2015";
DateTime ActualStartDate = DateTime.Parse(StartDate);
DateTime ActualEndDate = DateTime.Parse(EndDate);
ActualEndDate = new DateTime(ActualEndDate.Year, ActualEndDate.Month, DateTime.DaysInMonth(ActualEndDate.Year, ActualEndDate.Month));
var diff = Enumerable.Range(0, Int32.MaxValue)
.Select(e => ActualStartDate.AddMonths(e))
.TakeWhile(e => e <= ActualEndDate)
.Select(e => e.ToString("MMMM"));
It gives you output as {"March","April","May"}