The .NET Framework has no native support for the ZIP format. There are various options available. You can create your own ZIP library in J# using the Java class library's ZIP support, then reference that library in your VB projects. You can also use the open source #ZipLib, which is written in C#, and reference that in your VB code. There are also various commercial components available to do the job.
Another option is to create your own TAR library to put all files in the one TAR archive and then use .NET's native GZIP support to create a tarball, i.e. a GZIPped TAR file. This is not a viable option if you specifically need a ZIP file, but most commercial compression tools will read TGZ files.