Entity Framework with Include and Select together

may be:

var program = (from p in mEntities.Programs
          where p.Id ==Id
          select new {
             Program = p,
             ProgramFoodTypes = from pf in p.ProgramFoodTypes
                                where pf.IsActive
                                select pf,                  
             ProgramFoods = p.ProgramFoods.Select(y => new {
                 Food = y.Food,
                 Type = y.FoodType
             }) 
          }).ToArray().Select(m => m.Program);

For your second solution, I think you can use:

var program = (from p in mEntities.Programs
                  .Include(p => p.ProgramFoods.Select(f => f.Food))
                  .Include(p => p.ProgramFoods.Select(f => f.FoodType))
               where p.Id == Id
               select new {
                  Program = p,
                  ProgramFoodTypes = from pf in p.ProgramFoodTypes
                                     where pf.IsActive
                                     select pf,                  
                  p.ProgramFoods 
               }).ToArray().Select(m => m.Program);

update: Since you're using anonymous type in your linq query, Include statements are dismissed.
You'd have to load all related ProgramFoodTypes on client side, and then do the filtering:

var program = mEntities.Programs
                   .Include(p => p.ProgramFoodTypes)
                   .Include(p => p.ProgramFoods.Select(f => f.Food))
                   .Include(p => p.ProgramFoods.Select(f => f.FoodType))
                   .SingleOrDefault(m => m.Id == Id);

program.ProgramFoodTypes = program.ProgramFoodTypes.Where(pft => pft.IsActive);  

You can use AsNoTracking() or clone the returned Program object in a new object in case you want to make sure your data will be intact on db-side.