Under proposals published in June, Ofsted, the Care Quality Commission (CQC), Her Majesty's Inspectorate of Constabulary (HMIC), Her Majesty's Inspectorate of Probation and, where appropriate, Her Majesty's Inspectorate of Prisons will work together on targeted "integrated" inspections of children's services from April 2015.
But the ADCS has warned that the proposals - which involve separate judgments from each inspectorate on their respective agencies - "lack credibility" and highlight how "disunited" the individual inspectorates are.
Alan Wood, ADCS president, said the association is in favour of multi-agency inspection, but feels the current proposals will not deliver it successfully.
"The interactions between agencies and the impact of these actions on individual children and families are highly interdependent," he said. "However, the complexity of judging multi-agency child protection work and the incomparability of the resulting outcomes of the proposed integrated inspections has led us to conclude that the goal is not currently attainable as the inspection bodies cannot agree a common framework.
"The proposals in the consultation lack credibility and show how disunited the inspectorates are. They should be put on hold pending further discussions with local authorities, other agencies and inspectorates, particularly in the light of the recently published Jay report on child sexual exploitation."
The ADCS also raised concerns about the scope of the inspections.
Its response to a consultation on the proposals, which closed on Friday (12 September), it said it is "not entirely clear" that the CQC intends to look at safeguarding and information sharing issues in relation to adult substance misuse and adult mental health or that HMIC will look at domestic abuse arrangements.
"These are critical areas in terms of local authority children's services' ability to respond and protect children from risk of harm/significant harm," the consultation response states.
"If there is to be a true evaluation of how agencies work together to protect children, these matters would be central."
The ADCS also said integrated inspections could "exacerbate" the problem of the quality and calibre of inspectors across the individual inspectorates and "inconsistent judgments".
As part of its submission, the association has proposed an alternative approach - calling for the existing single inspection framework to be shelved in favour of thematic inspections - on key issues such as child sexual exploitation, domestic violence, trafficked children, early intervention work with families by schools and children's health, alongside a "front door" inspection of multi-agency arrangements of contact, referral and assessment.
If the "front door" inspection identified "deep failings in practice or systemic failure", a full inspection would be triggered.
"Our belief is the current single inspection framework should be stood down by the end of 2015, with this model phased in to be operative from 2016," Wood said.
Wood first called for a "two-tier" inspection system at the ADCS conference in July.
Under the current proposals, the new multi-agency inspections will run alongside Ofsted's current three-year cycle for its single inspection framework for rating children's services - which was introduced in November 2013 and is due to be completed in November 2016.
Between 20 and 25 local authorities, around one in six of all top-tier authorities in England, are due to be inspected in the 19-month period between April 2015 and November 2016.
Those targeted will primarily be authorities where Ofsted is returning following a previous "inadequate" rating, as well as those where other inspectorates have concerns.
It had initially been planned to introduce multi-agency inspections - which would have resulted in a single report with an overall effectiveness judgment - in June 2013, but the plans were delayed following findings from the initial pilots.