CONSENT OF INDEPENDENT REGISTERED PUBLIC ACCOUNTING FIRM

     We have issued our report dated April 22, 2008, accompanying the financial
statements of Florida Insured Municipals Income Trust, Series 129 (included in
Insured Municipals Income Trust and Investors' Quality Tax-Exempt Trust,
Multi-Series 329) as of December 31, 2007, and for each of the three years in
the period then ended and the financial highlights for each of the five years in
the period ended December 31, 2007, contained in this Post-Effective Amendment
No. 8 to Form S-6 (File No. 333-88895) and Prospectus.

     We hereby consent to the use of the aforementioned report in this
Post-Effective Amendment and Prospectus and to the use of our name as it appears
under the caption "Other Matters-Independent Registered Public Accounting Firm".

                                                  GRANT THORNTON LLP