Multidimensional indices in databases
Oracle has an index type called a Bitmap Index which it describes as...


  A database index in which the database
  stores a bitmap for each index key
  instead of a list of rowids.


If a table has a bitmap index or a hint is used, it can use a bitmap access plan on regular B-tree indexes.  Bitmap indexes can be joined, union-ed, and intersected.

There is an excellent explanation at use-the-index-luke.com where it includes the following implementations of combining multiple B-Tree indexes:


  DB2:
  DB2 supports multiple index access on
  LUW 9r7 (using a dynamic bitmap) and
  on zOS v10.
  
  MySQL:
  MySQL has an index merge optimization
  starting with release 5.0.
  
  Oracle
  The Oracle database uses BITMAP
  CONVERSIONs to combine multiple indexes on the fly (introduced with
  9i).
  
  PostgreSQL
  PostgreSQL uses bitmaps to combine multiple indexes since version 8.1.
  
  SQL Server
  SQL Server can use multiple indexes ("Index Intersect") starting with V7.0 using a hash algorithm.


See also this StackOverflow question in which the first answer says that SQL Server does something similar to Bitmapped indexes using index intersection.

Efficient and Flexible Bitmap Indexing for Complex Similarity Queries is the closest reference I have found associating Bitmapped indexes with the word multidimensional.  Multidimensional seems to be more of a way to use indexes rather than an attribute of them.