Viola,
Yes, this is common in many organizations. There are several things you can do to help build a partnership with Admissions. Both departments have the best interests of the student in mind, but once everyone realizes that both jobs are similar it will be easier to move forward. Both CS and Admissions are relationship builders, both reach out to their clients (prospective students and prospective employers), via phone calls and then arrange meetings. Both teams have goals and outcomes they are working towards and both teams can be motivated and encouraged in the same way.
Think of ways the two departments can help each other. CS can attend Admissions meetings and update the Admissions team as to job opportunities that are available for students and share student success stories. Admissions can then share this information during their interviews with prospective students for a more impactful interview. CS can attend Admission open houses and arrange for employers to be present to talk to prospective students and their families. Since the Admissions team often has strong relationships with students once they enroll, Admission team members can help CS contact hard to reach graduates, or can assist in counseling students /graduates who are not taking advantage of job opportunities being offered to them. The Director of Admissions can do phone training or training on how to overcome objections with the CS team. These are just a few best practices ideas to help CS and Admissions work together.
Continue to look for ways the two departments can assist each other. Changing the culture of an organization won't happen overnight, but with some patience and persistence you can make a difference.
Sheri Leach